Question

Suppose you gather the following test scores from you fellow students: 92,71,67,81,73,90,76,76,85,77,62,99.
A.The upper quartile is 85
B.The interquartile range is 15.5
C.The lower quartile is 71
D.The median quartile is 76

Answer 1

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

62   67   71   73   76   76   77   81   85   90   92   99   

So, the bottom half is

62   67   71   73   76   76   

The median of these numbers is 72.

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

62   67   71   73   76   76   77   81   85   90   92   99   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

62   67   71   73   76   76   77   81   85   90   92   99   

So, the upper half is

77   81   85   90   92   99   

The median of these numbers is 87.5.

The interquartile range is the difference between the third and first quartiles.

The third quartile is 87.5.

The first quartile is 72.

The interquartile range = 87.5 - 72 = 15.5.

Hence here correct answer is B.The interquartile range is 15.5